### Theory:

**The volume of irregularly shaped objects**There is no exact formula to measure irregularly shaped objects, but there are some methods to do it. Since volume is the total space occupied by an object, the volume of a small irregular piece of stone can be found by the water displacement method.

**Water displacement method**

The volume is determined using a measuring cylinder, a piece of stone and water.

- A measuring cylinder with markings is filled with \(150\ ml\) of water.
- A stone is tied with a piece of thread and immersed completely into the water.
- When the stone is immersed, the level of water eventually increases.
- The stone occupies the space inside the cylinder by displacing some amount of water. This makes the water level rise.

**Inference**

The volume of water displaced will be equal to the volume of space occupied by the stone in the container. This technique is known as the water displacement method and was found by Archimedes.

**Amount of water displaced by the stone**

Assume that the water level was \(150\ ml\) initially. After immersing a piece of stone, imagine the water level rises to \(180\ ml\). Then,

Volume of the water displaced \(=\) \(180\ ml\) \(-\) \(150\ ml\) \(=\) \(30\ ml\)

\(1\ ml\) \(=\) \(1\ cm^3\)

\(30\ ml\) \(=\) \(30\ cm^3\)

Volume of stone \(=\) \(30\ cm^3\)

\(30\ ml\) \(=\) \(30\ cm^3\)

Volume of stone \(=\) \(30\ cm^3\)

**Volume of gas**

Like liquids, gases also fill the container into which they are placed. However, gases can be compressed and can be made to occupy lesser space - for example, an LPG gas cylinder. Hence, calculating the volume of gas is different from that of the volume of solids and liquids.

Liquids and gases can be measured in \(litres\) and can be expressed in \(cubic\) \(metre\) or \(m^3\).

$\begin{array}{l}1\phantom{\rule{0.147em}{0ex}}{m}^{3}=1\phantom{\rule{0.147em}{0ex}}\mathit{kilolitre}(\mathit{kl}\phantom{\rule{0.147em}{0ex}}\mathit{or}\phantom{\rule{0.147em}{0ex}}\mathit{kL})\\ 1\phantom{\rule{0.147em}{0ex}}{\mathit{cm}}^{3}=1\hspace{0.17em}\mathit{millilitre}(\mathit{ml}\phantom{\rule{0.147em}{0ex}}\mathit{or}\phantom{\rule{0.147em}{0ex}}\mathit{mL})\\ 1\hspace{0.17em}{\mathit{mm}}^{3}=1\hspace{0.17em}\mathit{microlitre}(\mu l\phantom{\rule{0.147em}{0ex}}\mathit{or}\phantom{\rule{0.147em}{0ex}}\mathit{\mu L})\end{array}$

Important!

One of the tiny unit for the measurement of liquid is \(microlitre\) ($\mathrm{\mu}l$).

$1\phantom{\rule{0.147em}{0ex}}\mathit{litre}\phantom{\rule{0.147em}{0ex}}(l)=1000000\hspace{0.17em}\mathit{microlitre}(\mu l)$

**Think and answer!**

Three vessels of different shapes are filled with water. Just by looking at the vessels, can you guess which one contains more amount of water? If not, how to measure the volume of the water in the given vessels experimentally?

A large measuring jar is taken. Now, the liquid in the first vessel is poured into the jar, and the reading is noted. Then, empty the measuring jar and repeat the same measuring technique for the other two containers. By comparing the readings, the volume of water in the given vessels can be easily found.

Reference:

https://upload.wikimedia.org/wikipedia/commons/1/17/Displacement_measurement.png